Deformation estimation is the foundation of emerging techniques that image the mechanical properties of soft tissues. We will describe theoretical analysis and experimental results for a technique of phase-based ultrasonic deformation estimation we call Weighted Phase Separation. Numerous phase-based algorithm variants have been tested on simulated RF data from uniform scatterer fields, subject to a range of uniform strain deformations. The results support the theory that underlies the new procedure, and also highlight the factors that may be considered in the design of high performance deformation estimators for practical applications. Background prior art can be found in U.S. Pat. No. 6,520,913, US 2005/165309 and US 2003/0200036.
Ultrasonic imaging of tissue mechanical properties is a growing field in which there are many competing approaches. The majority of schemes require high accuracy estimation of the small deformations that occur between successive frames in an ultrasound scan, although a smaller set of alternatives work in conjunction with conventional Doppler motion estimation. Most systems employ a conventional two-dimensional ultrasound scanner, and the aim of deformation estimation is to produce an array of one- or two-dimensional displacement estimates, which may be thought of as noisy samples from the displacement field over a fine grid of locations throughout each frame. The recorded displacement estimates are sometimes displayed directly as displacement images, but it is more common to produce strain images by taking spatial derivatives of the displacement. There also exist more elaborate analyses that aim at displaying quantitative estimates of the mechanical properties of the underlying tissue. This can be tackled, for example, by solving the inverse problem for the elasticity field when deformation data has been recorded under a known static load. Alternatively, elastic moduli can be estimated from a record of wavefront propagation when low frequency shear waves are transmitted through the region of interest.
Whichever techniques for analyzing deformation data become clinically important, the quality of the results from high level analysis will depend to a large degree on the accuracy of the underlying deformation estimation. Moreover, it is desirable that this estimation be performed at low computational cost.
It is helpful at this point to introduce some of the terminology generally used in ultrasound imaging. An ultrasound imaging system generally employs a one-dimensional or two-dimensional ultrasonic transducer array (although sometimes only a single transducer may be employed), the array comprising typically 20 to 256 transducers in each dimension. Each transducer acts as both a transmitter and a receiver. The transducers are generally driven by a pulse of RF energy, typically in the range 1-20 MHz; the signal may be considered narrow band in the sense that a pulse is sufficiently long to include a number of RF wavelengths thus having a relatively well-defined frequency. The ultrasound transducer array is usually coupled to the tissue under investigation by an ultrasound gel or water; typically the ultrasound penetrates a few centimeters, for example up to 25 cm, into the tissue under investigation, and the transducer array scans a region of a few centimeters in a lateral direction. The axial resolution is generally much greater than the lateral resolution, for example of the order of 1000 samples (in time) as compared with of the order of 100 lines laterally. So-called A-lines run actually from each transducer into the tissue under investigation; a so-called B-scan or B-mode image comprises a plane including a plurality of A-lines, thus defining a vertical cross section through the tissue. A B-scan is typically presented as a two-dimensional brightness image. A two-dimensional transducer array may be used to capture perpendicular B-scan images, for example to provide data for a three-dimensional volume.
A captured image is generally built-up by successively capturing data from along each of the A-lines in turn, that is by capturing a column of data centred on each ultrasonic transceiver in turn (although beam steering may be employed). However, when capturing data from a particular line, preferably a set of the transducers is driven, with gradually increasing phase away from the line on which the transducer is centred so as to create an approximately spherical ultrasonic wavefront converging on a focus on the line under investigation. The signals received from the transducers are summed with appropriate amplitude and phases to reconstruct the line data. This provides an RF (radio frequency) output which is usually time-gain compensated (because the amplitude of the received signal decreases with increasing probed depth) before being demodulated, optionally log-weighted and displayed as B-scan. Often the RF data is digitised at some point in the processing chain, for example prior to the demodulation, the remainder of the processing taking place in the digital domain. A pair of analogue-to-digital converters is typically employed to provide in-phase and quadrature digitised signal components so that phase data is available.
An outline block diagram of an ultrasonic imaging system suitable for implementing embodiments of the invention is shown in FIG. 1. This Figure merely illustrates one example of an imaging system, to assist in understanding the context in which embodiments of the invention may operate; the skilled person will understand that there are many other types of ultrasonic (and other) imaging systems with which embodiments of the invention may be employed.
We will describe how at least one-dimensional image data captured by a pulse-echo technique, in particular an ultrasonic imaging system, can be processed to determine deformation (displacement) data. The ultrasonic image data to be processed comprises digitised RF signal data as shown, optionally with pre-processing in the analogue domain. (Where pre-processing is employed it may take many forms, just one example of which is shown in the Figure). Broadly speaking the demodulated data may be processed by envelope detection and log weighting to provide a B-mode display and/or strain determination may be employed to provide a strain display. The demodulation illustrated in FIG. 1 extracts the amplitude (envelope) and phase information of the RF signal in a conventional manner and the signal is digitised after demodulation so that the processed RF signal comprises a demodulated baseband signal; in other systems the RF signal may be digitised prior to demodulation.
A digitised I and Q (in-phase and quadrature) signal is frequently available in conventional ultrasonic imaging equipment and, conveniently, embodiments of the invention described later may be implemented by processing this signal using a suitably programmed general purpose computer or digital signal processor (DSP) and/or by using dedicated hardware.
In the description which follows it is often convenient to refer to samples in time rather than explicitly to position data, but typically a direct relationship is assumed between these two variables (position=velocity×time) assuming a typical speed of sound. Thus, effectively, these two variables are interchangeable. For human tissue the speed of sound is normally taken as 1540 m/s (the speed for water at 49° C.), which is accepted as a good estimate; for other materials other speeds may be employed. Similarly in the discussion which follows we will generally refer to axial strain (because the resolution of a system is typically highest in the axial or A-line direction) but it will be appreciated that the techniques we describe are also applicable to lateral strain in one or two dimensions (with a two-dimensional array), albeit normally with reduced precision because of the reduced number of samples.
We consider the task of estimating the deformation between a pair of RF ultrasound frames acquired pre- and post-deformation, when in general displacement is a continuously varying function of location. Displacement may be estimated by positioning a window over a small section of data in the pre-deformation frame and locating the closest matching window in the post-deformation frame. The displacement estimate is the difference between the pre- and post-deformation window positions. The task of window matching entails adjusting the post-deformation window position in order to find the optimum in a measure of signal similarity. One measure is the correlation coefficient, although similar performance may be obtained from techniques employing alternative measures such as the sum of squared differences (F. Viola and W. F. Walker, “A comparison of the performance of time-delay estimators in medical ultrasound”, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 50(4):392-401, April 2003) and the phase of the complex cross-correlation function (X. Chen, M. J. Zohdy, S. Y. Emelianov, and M. O'Donnell, “Lateral speckle tracking using synthetic lateral phase”, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 51(5):540-550, May 2004; M. O'Donnell, A. R. Skovoroda, B. M. Shapo, and S. Y. Emelianov, “Internal displacement and strain imaging using ultrasonic speckle tracking”, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 41:314-325, May 1994). The estimation procedure is repeated throughout a grid of locations, as above, until the displacement field has been adequately sampled.
The window matching approach to deformation estimation is sometimes problematic: pre- and post-deformation windows often match poorly, because deformation may not be negligible on the scale of the individual windows. Thus the post-deformation signals may be warped to increase the correlation between pre- and post-deformation windows, to implement an “adaptive” strain estimator. The simplest adaptive method is to apply a uniform stretch to the post-deformation signal, aiming to reverse part of the signal transformation that has actually taken place. Deformation data from adaptive strain estimators are measurably less noisy than standard displacement estimation, but the improvement is accompanied by a considerable increase in computational cost.
We have recently noted, however, that window matching approaches can be enhanced: Since finite length windows are used to produce displacement estimates with low noise, the accuracy of the data can be improved by estimating the location at which the displacement estimate is valid. Thus, in this approach, each deformation datum comprises an estimate of the displacement location in addition to the displacement itself. Implicitly assuming that the location is the window centre, results in an “amplitude modulation” artefact with the RF signal amplitude modulating the strain image. For this reason, we call our location estimation technique Amplitude Modulation Correction (AMC). We have demonstrated that AMC yields better performance at lower computational cost than adaptive strain estimation (J. E. Lindop, G. M. Treece, A. H. Gee, and R. W. Prager, “Estimation of displacement location for enhanced strain imaging”, Technical Report CUED/F-INFENG/TR 550, Cambridge University Department of Engineering, March 2006). Further details of AMC can be found in our UK patent application no. 0606125.3 filed on 28 Mar. 2006 hereby incorporated by reference in its entirety.
AMC can be implemented particularly easily in conjunction with phase-based displacement estimators and here we present further analysis of phase-based deformation estimation. Both theoretical and empirical methods are employed for the derivation and assessment of new phase-based deformation estimators. In particular, we introduce a new family of highly versatile algorithms which we refer to as Weighted Phase Separation (WPS). It is shown that the WPS framework can reproduce the performance of conventional phase-based methods, but WPS can also be adapted when different properties are required. The specific embodiments we describe consider deformation estimation in the axial direction, which is usually the most important: the accuracy is superior because RF ultrasound signals have far lower lateral and elevational bandwidth, and in many elasticity imaging schemes the largest deformations actually occur axially. However, the skilled person will readily appreciate that the teachings we present may be adapted for displacement estimation in other directions for multi-dimensional deformation estimation.